This invention is in the field of laboratory analysis of the physical properties of samples of material. Embodiments of this invention are directed to an apparatus and method for obtaining a rock sample suitable for high-resolution tomography and analysis via direct numerical simulation.
Knowledge of the properties of the material of subsurface rock formations is important for assessing hydrocarbon reservoirs in the earth and formulating a development strategy regarding those reservoirs. Traditionally, samples of the rock formation of interest are subjected to physical laboratory tests to determine these material properties, such properties also referred to as physical or petrophysical properties. However these tests are typically time consuming and expensive. For example, the measurements of certain properties of a physical rock sample require full water saturation of the sample, which can take an extremely long time if the rock has low permeability. Not only are the results not available in a timely fashion, but these tests necessarily occupy laboratory equipment over the duration of the experiment, limiting the sample throughput and thus the number of samples that can be measured in a reasonable time. It is desirable to improve the timeliness of analysis results and thus accelerate the development cycle, and also to increase the number of samples analyzed to improve the statistical confidence of the analysis results.
Direct numerical simulation of material properties from digital images of rock is a recent technology for determining the material properties of rock samples. According to this approach, an x-ray tomographic image is taken of a rock sample to produce a digital image volume representative of that sample. A computational experiment is then applied to the digital image volume to simulate the physical mechanisms from which the physical properties of the rock can be measured. Properties of the rock such as porosity, absolute permeability, relative permeability, formation factor, elastic moduli, and the like can be determined using direct numerical simulation. In particular, direct numerical simulation is capable of estimating the material properties of difficult rock types, such as tight gas sands or carbonates, within a timeframe that is substantially shorter than that required for the corresponding physical measurement. In addition, test equipment is not occupied over long periods of time according to this technique, as the analogous numerical conditions to the physical experiment can be immediately applied by the computer simulation software.
The quality of the tomographic image of the rock sample is necessarily a significant factor in the accuracy of the estimate of the material properties. X-ray tomography is based on the detection of differences in the attenuation of the incident energy by the material components (e.g., matrix space vs. pore space, or differences in rock composition). To obtain accurate estimates of the material properties, it is important that these attenuation values accurately represent the structure and material of the rock. Artifacts due to “beam hardening”, or the preferential absorption of low energy photons in irregularly-shaped rock samples, degrade the accuracy of the tomographic image. More specifically, beam hardening results from the mechanisms of photoabsorption, scattering, and photoelectric effect involved that attenuate the X-rays. Because lower energy X-rays are more affected by these mechanisms than are higher energy X-rays, the beam is said to “harden” in that the mean energy of the beam increases upon passing through the sample. The shape of the sample can cause this beam hardening to vary with position within the sample. If the cross-section of the sample is regularly shaped, for example circular, post-processing of the attenuation data readily compensates for these non-uniform beam hardening effects. However, if the sample has an irregular cross-section or otherwise has a variable thickness (e.g., polygonal cross-section), this post-processing is more difficult if not impossible. If beam hardening is not properly compensated, the digital image volume may not accurately represent the material properties of the rock.
Another factor that affects tomographic image quality is the resolution of the image, namely the size of the smallest detail distinguishable by the imaging. Image resolution is controlled by characteristics of the acquisition system components and their spatial configuration relative to the sample. Cross sectional sample size impacts image resolution, as the minimum voxel size corresponds to the longest lateral dimension of the acquired image divided by the number of detector pixels representing that longest lateral dimension. Samples in which the longest lateral dimension is relatively small (e.g., 2 mm) can thus be imaged at higher image resolution, or smaller voxel size. It is also important for the image volume “field of view” to be maximized so as to cover the largest possible volume of rock under full illumination (i.e., the sample remains in the field of view of the detector at all times).
Considering all of these factors, it has been observed that cylindrical samples of rock of relatively small diameter (e.g., on the order of 2 to 3 mm) provide the optimal cross-sectional shape and size for obtaining high quality tomographic images for direct numerical simulation using modern technology. These small cylindrical samples provide a regularly shaped cross-section for which beam hardening is minimized and correctable, voxels of smaller size for improved resolution, and good field of view under full illumination.
In addition, the length of the cylindrical sample in the axial dimension has also proven to be important. It has been observed that the longest possible axial extension of the sample maximizes the volume of material that is continuously imaged by a helical image acquisition system, and also saves time in sample preparation and placement for standard (circular) image acquisition system geometries. The volume of material that is imaged should especially be maximized for the case of coarsely-grained and heterogeneous rock, to obtain an imaged volume that is statistically representative of the formation from which the sample was taken.
Considering these factors in combination, a cylindrical rock sample of small cross-section (e.g., less than 3 mm) and relatively long axial length (e.g., greater than 10 mm) is desirable for tomographic imaging for direct numerical simulation, using conventional image acquisition systems. Meeting these geometrical requirements necessitates the cutting of the sample that is to subsequently be imaged from a larger sample (e.g., a core sample, drill cuttings, etc.) that is itself obtained from the sub-surface formation of interest.
In addition to these geometric requirements, accurate direct numerical simulation requires that the integrity of the material of the sampled formation be maintained in the sample to be imaged. More specifically, the preparation of the sample should not remove granular material from the edges of the sample volume, create fractures in the grains or matrix that were not previously present, loosen grains at the sample perimeter, or otherwise deform grain shapes or pore space characteristics. This requires cleanly, directly, and non-destructively cutting through individual grains of the rock.
Conventionally, the coring of a volume of rock to obtain a small cylindrical sample suitable for imaging has been performed by drilling with a hollow drill bit, commonly referred to as a “core bit”. It has been observed that this coring technique is suitable for reliably obtaining samples as small as 4 mm in diameter from some rock types. At smaller diameters, however, this approach tends to strip or fracture grains of the rock, which destroys the sample. In addition, coring in this manner has proven to be unsuitable for certain rock types, particularly rock that contains granular or sedimentary material that is not highly consolidated.
Conventional core bits also are limited in the axial length of the thin cylindrical sample that is obtained. Typically, the maximum axial length of a 3 mm core sample that can be obtained by a core bit is on the order of 5 mm. As mentioned above, it is desirable to obtain samples for imaging that are significantly longer than 5 mm, especially for use in connection with helical image acquisition systems.
Another conventional approach to the preparation of samples for tomographic imaging in the direct numerical simulation context is the cutting of rock with a diamond disc saw. This approach can obtain relatively long samples of small cross-section along the axial dimension, with minimal degradation of the sample at its cut edges. But because the disc saw is only able to cut along a two-dimensional plane, the prepared sample will have a rectangular cross-section, which results in significant loss of the imaged volume necessitated by compensation for beam hardening, given the non-uniform distances traveled by the incident energy in the sample. For example, the resulting image volume from a parallelepiped sample contains only about 60% of the voxels that can be obtained from a similarly sized cylindrical sample. Other disadvantages resulting from the parallelepiped sample shape include poor compatibility of the sample with flow or pressure cells, and the inability to perform “region of interest” (ROI) evaluations.
By way of further background, the preparation of samples for microscopy using a diamond wire saw is known in the art. One example of a conventional diamond wire saw uses a thin stainless steel wire onto which industrial diamonds of varying grit size are embedded. The cutting motion can be either reciprocating or in one direction. Examples of these conventional diamond wire saws include those available from Well Diamond Wire Saws, Inc.